Thermally assisted magnetization reversal in the presence of a spin-transfer torque

By Z. Li, Shufeng Zhang. 2003

364 citations recorded by the source corpus.

We propose a generalized stochastic Landau-Lifshitz equation and its corresponding Fokker-Planck equation for the magnetization dynamics in the presence of spin-transfer torques. Since the spin-transfer torque can pump a magnetic energy into the magnetic system, the equilibrium temperature of the magnetic system is ill defined. We introduce an effective temperature based on a stationary solution of the Fokker-Planck equation. In the limit of high-energy barriers, the law of thermal agitation is derived. We find that the N\'eel-Brown relaxation formula remains valid as long as we replace the temperature by an effective one that is linearly dependent on the spin torque. We carry out the numerical integration of the stochastic Landau-Lifshitz equation to support our theory. Our results agree with existing experimental data.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/aa8f2cb838cb22f4e42736359af5b16f4e3491f2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Hideo Ohno
2. A. Manchon
3. Y. Tserkovnyak
4. M. Chshiev
5. Bernard Dieny
6. A. Brataas
7. D. Ralph
8. G. Bauer

In Condensed Matter Physics

1. Y. Tserkovnyak
2. A. Brataas
3. M. Chshiev
4. B. Halperin
5. G. Bauer
6. A. Manchon
7. Bernard Dieny
8. Hideo Ohno

Citations in the corpus

• Bias-voltage dependence of perpendicular spin-transfer torque in asymmetric MgO-based magnetic tunnel junctions (2009, methodology): “To determine the bias dependence of , we used the thermal activation mode”
• Spintronics (2015, background): “The MTJ-based HDD read head promises to achieve over 200Gbit in−2 recording density and 1Gbit/second data rate.”
• Spin-transfer effects in nanoscale magnetic tunnel junctions (2004, background): “The switching probability per unit time follows an Arrhenius law, where the energy barrier, Ea, varies with the current as Ea(I = 0) (1− I/Ic,o) [56, 58, 62, 63].”
• MgO/CoFeB/Ta/CoFeB/MgO Recording Structure in Magnetic Tunnel Junctions With Perpendicular Easy Axis (2013, background): “To evaluate , switching current dependence on the pulse current duration [27] (0.”
• Spin-torque building blocks. (2014, methodology): “3 torque strength and thus the mean time spent in each state can be tuned [20], as shown in Fig.”
• Nonlocal magnetization dynamics in ferromagnetic heterostructures (2004, background): “The current-induced dynamics of domain walls (Barnes and Maekawa, 2005; Li and Zhang, 2004a; Tatara and Kohno, 2004 and references therein) are also beyond the macrospin considerations central to this review.”
• Perpendicular magnetic anisotropy at transition metal/oxide interfaces and applications (2017, methodology): “Magnetization will be reversed when the injected current has the appropriate direction (electrons flowing from the reference layer to the storage layer to induce a switch from the antiparallel magnetic configuration (AP) to the parallel one (P) and flowing in the opposite direction to switch from P ”